Introduction to LRFD, Loads and Loads Distribution

Introduction to LRFD, Loads and Loads Distribution Thomas K. Saad, P.E. Federal Highway Administration Chicago, IL Evolution of Design Methodologies SLD Methodology: (f t ) D + (f t ) L 0.55F y, or 1.82(f t ) D + 1.82(f t ) L F y LFD Methodology: 1.3[1.0(f t ) D + 5/3(f t ) L ] φf y, or 1.3(f t ) D + 2.17(f t ) L φf y LRFD Methodology: 1.25(f t ) D + 1.75(f t ) L φf y (φ by judgment) (φ by calibration) (new live-load model) Introduction to LRFD 1-1

Evolution of Design Methodologies (cont d) SLD does not recognize that some types of loads are more variable than others. LFD provides recognition that types of loads are different. LRFD provides a probability-based mechanism to select load & resistance factors. Evolution of Design Methodologies (cont d) As a result, LRFD achieves considerable improvement in the clustering of reliability indices versus the AASHTO Standard Specifications. RELIABILITY IDEX 5 4 3.5 3 2 1 RELIABILITY IDEX 0 0 30 60 90 120 200 SPA LEGTH (Feet) LFD LRFD Introduction to LRFD 1-2

Basic LRFD Design Equation Ση i γ i Q i φr n = R r Eq. (1.3.2.1-1) where: η i = η D η R η I η i 0.95 for maximum γ s η i = 1 < 1.00 for minimum γ s η η η D R γ i = Load factor φ = Resistance factor Q i = ominal force effect R n = ominal resistance R r = Factored resistance = φr n I LRFD Limit States The LRFD Specifications require examination of several load combinations corresponding to the following limit states: SERVICE LIMIT STATE relating to stress, deformation, and cracking FATIGUE & FRACTURE LIMIT STATE relating to stress range and crack growth under repetitive loads, and material toughness STREGTH LIMIT STATE relating to strength and stability - (COSTRUCTIBILITY) EXTREME EVET LIMIT STATE relating to events such as earthquakes, ice load, and vehicle and vessel collision Introduction to LRFD 1-3

3.3.2 Load and Load Designation STREGTH I : STREGTH II : STREGTH III : STREGTH IV : STREGTH V : SERVICE I : SERVICE II : SERVICE III : SERVICE IV : FATIGUE : without wind. owner design / permit vehicles without wind. wind exceeding 55 mph. very high dead-to-live load ratios. vehicular use with 55 mph wind. normal operational use of the bridge with a 55 mph wind and nominal loads. Also control cracking of reinforced concrete structures. control yielding of steel structures and slip of connections control cracking of prestressed concrete superstructures. control cracking of prestressed concrete substructures. repetitive vehicular live load and dynamic responses under a single truck. 3.3.2 Load and Load Designation DD = downdrag DC = dead load of structural components and nonstructural attachments DW = dead load of wearing surfaces and utilities EH = horizontal earth pressure EL = accumulated locked-in force effects resulting from the construction process, including the secondary forces from post-tensioning ES = earth surcharge load EV = earth fill vertical pressure BR = braking force CE = centrifugal force CR = creep CT = vehicular collision force CV = vessel collision force EQ = earthquake FR = friction IC = ice load IM = dynamic load allowance LL = live load LS = live load surcharge PL = pedestrian live load SE = settlement SH = shrinkage TG = temperature gradient TU = uniform temperature WA = water load and stream pressure WL = wind on live load WS = wind load on structure Introduction to LRFD 1-4

Permanent Loads (Article 3.5) Dead Load (Article 3.5.1): DC - Dead load, except wearing surfaces & utilities DC 1 - placed prior to deck hardening and acting on the noncomposite section DC 2 - placed after deck hardening and acting on the long-term composite section DW - Wearing surfaces & utilities acting on the longterm composite section Load Factors for Permanent Loads, γ p Load Factor Type of Load Maximum Minimum DC: Component and Attachments 1.25 0.90 DD: Downdrag 1.80 0.45 DW: Wearing Surfaces and Utilities EH: Horizontal Earth Pressure Active At-Rest EV: Vertical Earth Pressure Overall Stability Retaining Structure Rigid Buried Structure Rigid Frames 1.50 0.65 1.50 1.35 1.35 1.35 1.30 1.35 1.95 0.90 0.90 /A 1.00 0.90 0.90 0.90 Introduction to LRFD 1-5

Basic LRFD Design Live Load HL-93 -- (Article 3.6.1.2.1) Design Truck: or Design Tandem: Pair of 25.0 KIP axles spaced 4.0 FT apart superimposed on Design Lane Load 0.64 KLF uniformly distributed load or 25.0 KIP 25.0 KIP + 0.64 Kip/ft LRFD egative Moment Loading (Article 3.6.1.3.1) For negative moment (between points of permanent-load contraflexure) & interior-pier reactions, check an additional load case: 0.9 x > 50-0 Introduction to LRFD 1-6

LRFD Fatigue Load (Article 3.6.1.4.1) Design Truck only => w/ fixed 30-ft rearaxle spacing Placed in a single lane 1 Load Combinations and Load Factors Load Combination Limit State DC DD DW EH EV ES LL IM CE BR PL LS WA WS WL FR TU CR SH TG SE Use One of These at a Time EQ IC CT CV STREGTH-I γ p 1.75 1.00 - - 1.00 0.50/1.20 γ TG γ SE - - - - STREGTH-II γ p 1.35 1.00 - - 1.00 0.50/1.20 γ TG γ SE - - - - STREGTH-III γ p - 1.00 1.40-1.00 0.50/1.20 γ TG γ SE - - - - STREGTH-IV EH, EV, ES, DW DC OLY γ p 1.5-1.00 - - 1.00 0.50/1.20 - - - - - - STREGTH-V γ p 1.35 1.00 0.40 1.00 1.00 0.50/1.20 γ TG γ SE - - - - EXTREME-I γ p γ EQ 1.00 - - 1.00 - - - 1.00 - - - EXTREME-II γ p 0.50 1.00 - - 1.00 - - - - 1.00 1.00 1.00 SERVICE-I 1.00 1.00 1.00 0.30 0.30 1.00 1.00/1.20 γ TG γ SE - - - - SERVICE-II 1.00 1.30 1.00 - - 1.00 1.00/1.20 - - - - - - SERVICE-III 1.00 0.80 1.00 - - 1.00 1.00/1.20 γ TG γ SE - - - - FATIGUE-LL, IM & CE OLY - 0.75 - - - - - - - - - - - Introduction to LRFD 1-7

Resistance Factors (Article 6.5.4.2) Resistance factors, φ, for the strength limit state shall be taken as follows: For flexure φ f = 1.00 For shear φ v = 1.00 For axial compression, steel only φ c = 0.90 For axial compression, composite φ c = 0.90 For tension, fracture in net section φ u = 0.80 For tension, yielding in gross section φ y = 0.95 For bolts bearing on material φ bb = 0.80 For shear connectors φ sc = 0.85 For A 325 and A 490 bolts in shear φ s = 0.80 For block shear φ bs = 0.80 For web crippling φ w = 0.80 For weld metal in fillet welds: tension or compression parallel to axis of the weld same as base metal shear in throat of weld metal φ e2 = 0.80 Resistance Factors (Article 5.5.4.2) Resistance factor φ shall be taken as: For flexure and tension of reinforced concrete. 0.90 For flexure and tension of prestressed concrete. 1.00 For shear and torsion: normal weight concrete 0.90 lightweight concrete. 0.70 For axial compression with spirals or ties, except as specified in Article 5.10.11.4.1b for Seismic Zones 3 and 4 at the extreme event limit state.. 0.75 For bearing on concrete 0.70 For compression in strut-and-tie models 0.70 For compression in anchorage zones: normal weight concrete 0.80 lightweight concrete. 0.65 For tension in steel in anchorage zones.. 1.00 For resistance during pile driving.. 1.00 Introduction to LRFD 1-8

Structural Analysis & Evaluation (Article 4) Static Analysis (Article 4.6) Approximate Methods of Analysis (Article 4.6.2) Beam-Slab Bridges (Article 4.6.2.2) Live-Load Lateral Distribution Factors TABLE 4.6.2.2.1-1 COMMO DECK SUPERSTRUCTURES COVERED I ARTICLES 4.6.2.2.2 AD 4.6.2.2.3. SUPPORTIG COMPOETS TYPE OF DECK TYPICAL CROSS-SECTIO Steel Beam Cast-in-place concrete slab, precast concrete slab, steel grid, glued/spiked panels, stressed wood Closed Steel or Precast Concrete Boxes Cast-in-place concrete slab Open Steel or Precast Concrete Boxes Cast-in-place concrete slab, precast concrete deck slab Cast-in-Place Concrete Multicell Box Monolithic concrete Cast-in-Place Concrete Tee Beam Monolithic concrete Precast Solid, Voided or Cellular Concrete Boxes with Shear Keys Cast-in-place concrete overlay Precast Solid, Voided, or Cellular Concrete Box with Shear Keys and with or without Transverse Posttensioning Integral concrete Introduction to LRFD 1-9

For Moments Interior Beams Table 4.6.2.2.2b-1 Distribution of Live Loads Per Lane for Moment in Interior Beams. Type of Beams Concrete Deck, Filled Grid, Partially Filled Grid, or Unfilled Grid Deck Composite with Reinforced Concrete Slab on Steel or Concrete Beams; Concrete T- Beams, T- and Double T- Sections Applicable Cross-Section from Table 4.6.2.2.1-1 Distribution Factors a, e, k and also One Design Lane Loaded: i, j 0.4 0.3 0.1 S S K g if sufficiently 0.06 + 3 connected to 14 L 12.0Lts act as a unit Two or More Design Lanes Loaded: 0.6 0.2 0.1 S S K g 0.075 + 3 9.5 L 12.0 Lts use lesser of the values obtained from the equation above with b = 3 or the lever rule Range of Applicability 3.5 S 16.0 20 L 240 4.5 ts 12.0 4 b 10,000 K g 7,000,000 b = 3 otes: 1) Units are in LAES and not WHEELS! 2) o multiple presence factor Introduction to LRFD 1-10

For Shear Interior Beams Table 4.6.2.2.3a-1 Distribution of Live Load per Lane for Shear in Interior Beams. Type of Superstructure Concrete Deck, Filled Grid, Partially Filled Grid, or Unfilled Grid Deck Composite with Reinforced Concrete Slab on Steel or Concrete Beams; Concrete T-Beams, T-and Double T-Sections Applicable Cross-Section from Table 4.6.2.2.1-1 a, e, k and also i, j if sufficiently connected to act as a unit One Design Lane Loaded S 0.36 + 25.0 Two or More Design Lanes Range of Loaded Applicability 2.0 S S 3.5 S 16.0 0.2 + 12 35 20 L 240 4.5 t 12.0 b s 4 Lever Rule Lever Rule b = 3 otes: 1) Units are in LAES and not WHEELS! 2) o multiple presence factor Live-Load Distribution Factors Design Example Introduction to LRFD 1-11

Example POSITIVE FLEXURE (ED SPA) Calculate Kg: n = 8.A. is 39.63 in. from the top of the steel. e g e K g g 9.0 = + 3.5 + 39.63 1.0 = 46.63in. 2 = n I 2 2 6 4 ( + Ae ) = 8( 62,658+ 75.25( 46.63) ) = 1.81x 10 in. g Introduction to LRFD 1-12

M+, Interior Girder t S S Article 4.6.2.2.2b: One lane loaded: S 0.06 + 14 0.4 Two or more lanes loaded: S 0.075 + 9.5 L S L 0.6 0.3 S L Kg 12.0Lt 0.2 3 S Kg 12.0Lt 3 S 0.1 0.1 Live-Load Distribution Factors M+, Interior Girder - (cont d) One lane loaded: 12.0 0.06 + 14 0.4 12.0 140.0 0.3 1.81x 10 12.0 6 ( 140.0)( 9.0) 3 0.1 = 0.528 lanes Two or more lanes loaded: 12.0 0.075 + 9.5 0.6 12.0 140.0 0.2 1.81x 10 12.0 6 ( 140.0)( 9.0) 3 0.1 = 0.807 lanes (governs) Introduction to LRFD 1-13

V, Interior Girder Table 4.6.2.2.3a-1 One lane loaded: S 0.36 + 25.0 12.0 0.36 + = 0.840 lanes 25.0 Two or more lanes loaded: 0.2 + S 12 S 35 12.0 12.0 0.2 + 12 35 2 2 = 1.082 lanes (governs) Live-Load Distribution Factors M-, Interior Girder L = 0.5(140+175) = 157.5 ft. One lane loaded: Two or more lanes loaded:. 12.0 0.06 + 14 12.0 0.075 + 9.5 0.6 0.4 12.0 157.5 12.0 157.5 0.2 0.3 2.65 x 10 12.0(157.5) 2.65 x 10 12.0(157.5) 6 ( 9.0) 3 6 ( 9.0) 0.1 3 0.1 = 0.524 lanes = 0.809 lanes (governs) Introduction to LRFD 1-14

Moments Exterior Beams Table 4.6.2.2.2d-1 Distribution of Live Loads Per Lane for Moment in Exterior Longitudinal Beams. Type of Superstructure Concrete Deck, Filled Grid, Partially Filled Grid, or Unfilled Grid Deck Composite with Reinforced Concrete Slab on Steel or Concrete Beams; Concrete T-Beams, T- and Double T- Sections Applicable Cross- Section from Table 4.6.2.2.1-1 a, e, k and also i, j if sufficiently connected to act as a unit One Design Lane Loaded Lever Rule Two or More Design Lanes Loaded g = e ginterior d e e = 0.77 + 9.1 use lesser of the values obtained from the equation above with b = 3 or the lever rule Range of Applicability -1.0 < de < 5.5 b = 3 otes: In beam-slab bridges with diaphragms or cross-frames, the distribution factor for the exterior beam shall not be taken to be less than that which would be obtained by assuming that the cross-section deflects and rotates as a rigid cross-section. R = L b X + L ext b 2 x e Live-Load Distribution Factors Shear Exterior Beams Table 4.6.2.2.3b-1 Distribution of Live Load per Lane for Shear in Exterior Beams. Type of Superstructure Concrete Deck, Filled Grid, Partially Filled Grid, or Unfilled Grid Deck Composite with Reinforced Concrete Slab on Steel or Concrete Beams; Concrete T- Applicable Cross- Section from Table 4.6.2.2.1-1 a, e, k and also i, j if sufficiently connected to act as a unit One Design Lane Loaded Lever Rule Two or More Design Range of Lanes Loaded Applicability g = e g interior -1.0 < d e < 5.5 de e = 0.6 + 10 Lever Rule b = 3 otes: In beam-slab bridges with diaphragms or cross-frames, the distribution factor for the exterior beam shall not be taken to be less than that which would be obtained by assuming that the cross-section deflects and rotates as a rigid cross-section. L X R = + b L ext b 2 x e Introduction to LRFD 1-15

M, Exterior Girder For bending moment (Article 4.6.2.2.2d): One lane loaded: Use the lever rule Consider multiple presence factors when: - # of lanes of traffic on the deck must be considered in the analysis (Art. 3.6.1.1.2) umber of Loaded Lanes Multiple Presence Factors "m" 1 1.20 2 1.00 3 0.85 > 3 0.65 = R x 9 / 12 Introduction to LRFD 1-16

M, Exterior Girder - (cont d) One lane loaded: Using the lever rule 9.0 12.0 = 0.750 Multiple presence factor m = 1.2 (Table 3.6.1.1.2-1) 1.2 ( 0.750) = 0.900 lanes umber of Loaded Lanes Multiple Presence Factors "m" 1 1.20 2 1.00 3 0.85 > 3 0.65 Live-Load Distribution Factors M, Exterior Girder - (cont d) Two or more lanes loaded: Modify interior-girder factor by e de e = 0.77 + (Table 4.6.2.2.2d-1) 9.1 2.0 e = 0.77 + = 0.990 9.1 0.990 ( 0.807 ) = 0.799 lanes ote: 1) The multiple presence factor is not applied. Introduction to LRFD 1-17

M, Exterior Girder - (cont d) Special Analysis: for beam-slab bridges with diaphragms or cross frames Assuming the entire cross-section rotates as a rigid body about the longitudinal centerline of the bridge, distribution factors for one, two and three lanes loaded are computed using the following formula: R = L b X + L ext b 2 x e Eq. (C4.6.2.2.2d-1) Live-Load Distribution Factors M, Exterior Girder - (cont d) Special Analysis: R = L b X + L ext b 2 x e Eq. (C4.6.2.2.2d-1) R L e x X ext b = reaction on exterior beam in terms of lanes = number of loaded lanes under consideration = eccentricity of a lane from the center of gravity of the pattern of girders (ft) = horizontal distance from the center of gravity of the pattern of girders to each girder (ft) = horizontal distance from the center of gravity of the pattern of girders to the exterior girder (ft) = number of beams or girders Introduction to LRFD 1-18

M, Exterior Girder - (cont d) One lane loaded: 15-0 R = 1 4 ( 18.0)( 15.0) + 2 18.0 2 2 ( + 6.0 ) = 0.625 m R = 1.2(0.625) = 0.750 lanes 1 R = L b X + ext b x L 2 e 18-0 umber of Loaded Lanes Multiple Presence Factors "m" 1 1.20 2 1.00 3 0.85 > 3 0.65 Live-Load Distribution Factors M, Exterior Girder - (cont d) Two lanes loaded: 15-0 L X ext R = + b b x 2 R = + 4 2 18.0 ( 18.0)( 15.0 + 3.0) 2 2 ( + 6.0 ) = 0.950 m R = 1.0(0.950) = 0.950 lanes (governs) 2 L 2 e umber of Loaded Lanes Multiple Presence Factors "m" 1 1.20 2 1.00 3 0.85 > 3 0.65 Introduction to LRFD 1-19

M, Exterior Girder - (cont d) Three lanes loaded: 15-0 - R = R = 3 4 m R = 0.85 3 L b X + ext b x (18.0 ) + 2 18.0 L 2 e ( 15.0 + 3.0-9.0) 2 2 ( + 6.0 ) ( 0.975) = 0.829 lanes = 0.975 umber of Loaded Lanes Multiple Presence Factors "m" 1 1.20 2 1.00 3 0.85 > 3 0.65 Live-Load Distribution Factors V, Exterior Girder - (cont d) For shear (Article 4.6.2.2.3b): One lane loaded: Use the lever rule 0.970 lanes Two or more lanes loaded: Modify interior-girder factor by e de e = 0.6 + 10 2.0 e = 0.6 + = 0.80 10 0.80 ( 1.082) = 0.866 lanes (Table 4.6.2.2.3b-1) Introduction to LRFD 1-20

V, Exterior Girder - (cont d) Special Analysis: The factors used for bending moment are also used for shear: One lane loaded: 0.750 lanes Two lanes loaded: Three lanes loaded: 0.950 lanes (governs) 0.829 lanes All factors used for both pos. & neg. flexure. SUMMARY Live-Load Distribution Factors Strength Limit State AASHTO LRFD - Positive Flexure: Interior Girder Exterior Girder Bending Moment 0.807 lanes 0.950 lanes Shear 1.082 lanes 0.950 lanes AASHTO LRFD - egative Flexure: Interior Girder Exterior Girder Bending Moment 0.809 lanes 0.950 lanes Shear 1.082 lanes 0.950 lanes Introduction to LRFD 1-21

Fatigue Limit State The fatigue load is placed in a single lane. Therefore, the distribution factors for onelane loaded are used. (see Article 3.6.1.4.3b) Multiple presence factors are not to be applied for fatigue. Thus, the distribution factors for one-lane loaded must be modified by dividing out the multiple presence factor of 1.2 specified for one-lane loaded. (see Article 3.6.1.1.2) SUMMARY Live-Load Distribution Factors Fatigue Limit State - Design Example AASHTO LRFD - Positive Flexure: Interior Girder Exterior Girder Bending Moment 0.440 lanes 0.750 lanes Shear 0.700 lanes 0.750 lanes AASHTO LRFD - egative Flexure: Interior Girder Exterior Girder Bending Moment 0.437 lanes 0.750 lanes Shear 0.700 lanes 0.750 lanes Introduction to LRFD 1-22

Skew Correction Factors For bending moment (Article 4.6.2.2.2e): The skew correction factor for bending moment reduces the live-load distribution factor. For skew angles less than 30, the correction factor is equal to 1.0. For skew angles greater than 60, the correction factor is computed using an angle of 60. The difference in skew angle between two adjacent lines of supports cannot exceed 10. Dead-load moments are currently not modified for the effects of skew. c 1 K = 0.25 Lt g 3 s 0.25 S L 0.5 Correction factor= 1 c 1 ( tanθ) 1. 5 (Table 4.6.2.2.2e-1) Live-Load Distribution Factors Skew Correction Factors (cont.) For shear (Article 4.6.2.2.3c): The skew correction factor increases the live-load distribution factor for shear in the exterior girder at the obtuse corner of the bridge. The correction factor is valid for skew angles less than or equal to 60. The factor may be conservatively applied to all end shears. Dead-load shears are currently not modified for the effects of skew. 3 Lt Correction factor = 1.0 + 0.20 s tanθ Kg (Table 4.6.2.2.3c-1) 0.3 Introduction to LRFD 1-23

Load for Optional Live-Load Deflection Evaluation (Article 3.6.1.3.2) The larger of: - The design truck, or - 25% of the design truck + 100% of the design lane load. Live-Load Deflection (Article 2.5.2.6.2) Use the SERVICE I load combination & multiple presence factors where appropriate. For straight-girder systems, all lanes should be loaded and all supporting components should be assumed to deflect equally. For composite design, the stiffness used for calculation of the deflection should include the entire width of the roadway, and may include the structurally continuous portions of the railings, sidewalks and barriers. Introduction to LRFD 1-24

Distribution Factor for Live-Load Deflection For the design example: L DF = m3 b 3 = 0.85 = 0.638 lanes 4 umber of Loaded Lanes Multiple Presence Factors "m" 1 1.20 2 1.00 3 0.85 > 3 0.65 Dynamic Load Allowance (Impact - IM) (Article 3.6.2.1) IM = 33% (for truck or tandem only; not for lane). Exceptions are: Deck joints: IM = 75% Fatigue limit state: IM = 15% Introduction to LRFD 1-25

QUESTIOS? Thomas Saad, P.E. FHWA, Suite 301 19900 Governors Drive Olympia Fields, IL 60461 Ph: 708.283.3521 E-mail: thomas.saad@fhwa.dot.gov Introduction to LRFD 1-26